text: I understand your concern for your cat, but as stated in the comments cats can keep warm quite well unless they are a breed without fur.
  The cat should not be in there at all
  If you still do not want to let your cat go into these rooms the only way is to close the door right behind you every time you go in or out. This can be relatively hard when carrying things, but to my experience it is the only way. The rooms you do not want your cats to be are the rooms they are most keen to get into.
  The cat can go in but what if she can not come back?
  If you are simply worried your cat might stay in these rooms for too long and you might not hear her trying to get back out, installing a cat flap in those doors can be an option.
  With a little bit of training she will be able to come back whenever she feels like it. There are also flaps that you can lock so they only open one way or not at all.
  Some things to keep in mind though:
  
  These cat flaps wont be the best at insulating so the area around them in the house might get cooler
  It is complicated to install them in e.g. a glass door
  
  But it would allow your cat to go in or out (depending on how you set the flap) without you needing to worry about temperature, hunger or cuddle needs.